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Method of variations of potential of quasi-periodic Schrodinger equation

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Jackson Chan

Mathematical Physics · Submitted 16 Oct 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0510057 (version 2)
Pith IDW2PUEXME, Pith's permanent record of this paper and its review
CitationJackson Chan. "Method of variations of potential of quasi-periodic Schrodinger equation." arXiv:math-ph/0510057 (2005). https://pith.science/paper/W2PUEXME
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,858 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.28 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the one-dimensional discrete quasi-periodic Schrodinger equation. We introduce the notion of variations of potential and use it to define "typical" potential. We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the one-dimensional discrete quasi-periodic Schrodinger equation. background 0.87 0.64 0.02 asserted 0.65
s1 We introduce the notion of variations of potential and use it to define "typical" potential. contribution 0.62 0.94 0.04 asserted 0.98
s2 We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies. result 1.00 0.94 0.88 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study the one-dimensional discrete quasi-periodic Schrodinger equation. We introduce the notion of variations of potential and use it to define "typical" potential. We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies.

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